When a lunar crater is formed by an impact, material from the depth of the crust is forced up and catapulted into the surrounding landscape, forming radial ejecta rays. The ejecta material has a higher albedo than the dark maria, making the rays plainly visible. Many lunar craters are associated with ray systems, most notably Copernicus, Kepler, Proclus and Tycho.
The Bessel Ray is a single ejecta ray running almost north-south through the middle of Mare Serenitatis. On it’s way it touches upon the Bessel crater (in the middle of the sketch), giving it it’s name.
Apparently there is some debate concerning the originator of the Bessel Ray: some suggest that it is associated with the nearby crater Menelaus (at the top of the sketch), others that it is part of the extensive ray system emanating from Tycho, far down south.
In an image from the Galileo spacecraft, the ray systems of Copernicus (left), Kepler (far left), Proclus (right) and Tycho (bottom) are prominent. Mare Serenitatis, with the Bessel Ray, can be seen near the center. Judging from the image the Bessel Ray seems to connect both with Menelaus (the bright spot on the southern shore of the mare) and with Tycho. I am not sure what to make of it, but if think I put my money on Tycho.